Imagine a particle of mass m and energy e in a potential well v (x), sliding frictionlessly back and forth between the classical turning points (call them a and b). classically, the probability of finding the particle in the range dx (if, for example, you took a snapshot at a random time t) is equal to the fraction of the time t it takes to get from a to b that it spends in the interval dx: rho(x)dx = dt t = (dt/dx)dx t = 1 v(x)t dx where v(x) is the speed, and t = z t 0 dt = z b a 1 v(x) dx . thus rho(x) = 1 v(x)t this is perhaps the closest analog to |ψ| 2 . (a) use conservation of energy to express v(x) in terms of e and v (x).